Home
Class 12
MATHS
Let A be a non-singular square matrix of...

Let A be a non-singular square matrix of order 3 `xx`3. Then |adj A| is equal to (a) `|A|` (B) `|A|^2` (C) `|A|^3` (D) `3|A|`

Text Solution

Verified by Experts

The correct Answer is:
(b)
`"(adj A).A=|A|."I_(3)=|A|[{:(1,0,0),(0,1,0),(0,0,1):}]`
`=[{:(|A|,0,0),(0,|A|,0),(0,0,|A|):}]`
`rArr" |dj A|.A| ="[{:(|A|,0,0),(0,|A|,0),(0,0,|A|):}]=|A|^(3)`
`rArr" |adj A |=|A|"^(2)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4.6|16 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4.4|5 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

Similar Questions

Explore conceptually related problems

Let A a non singular square matrix of order 3xx3 . Then |adjA| is equal to

Let A be a non-singular square matrix of order n. Then; |adjA| =

Let A be a square matrix of order 3xx3 , then |k A| is equal to (A) k|A| (B) k^2|A| (C) K^3|A| (D) 3k |A|

Let A be a square matrix of order 3xx3 , then |k A| is equal to(A) k|A| (B) k^2|A| (C) k^3|A| (D) 3k |A|

If A is a matrix of order 3xx3 , then |3A| is equal to………

Let A be an orthogonal non-singular matrix of order n, then |A-I_n| is equal to :

If A is a non singular square matrix then |adj.A| is equal to (A) |A| (B) |A|^(n-2) (C) |A|^(n-1) (D) |A|^n

If A is a non singular matrix of order 3 then |adj(adjA)| equals (A) |A|^4 (B) |A|^6 (C) |A|^3 (D) none of these

If A is a non singular square matrix 3 then |adj(A^3)| equals (A) |A|^8 (B) |A|^6 (C) |A|^9 (D) |A|^12

Let A be a square matrix of order 3 times 3 , then abs(kA) is equal to

NAGEEN PRAKASHAN ENGLISH-DETERMINANTS-Exercise 4.5
  1. Find the adjoint of each of the matrices [{:(1,2),(3,4):}]

    Text Solution

    |

  2. Find adjoint of the matrice in[1-1 2 2 3 5-2 0 1]

    Text Solution

    |

  3. Verify A (a d j A) = (a d j A) A = |A|I for [(2 ,3),(-4,-6)]

    Text Solution

    |

  4. Verify A" "(a d j" "A)" "=" "(a d j" "A)" "A" "=" "|A|"I" |1-1 2 3 0-...

    Text Solution

    |

  5. Find the inverse the matrix (if it exists)given in[2-2 4 3]

    Text Solution

    |

  6. Find the inverse the matrix (if it exists)given in[-1 5-3 2]

    Text Solution

    |

  7. Find the inverse the matrix (if it exists)given in[1 2 3 0 2 4 0 0 5]

    Text Solution

    |

  8. Find the inverse the matrix (if it exists)given in [1 0 0 3 3 0 5 2-1]

    Text Solution

    |

  9. Find the inverse the matrix (if it exists) given in[2 1 3 4-1 0-7 2 1]

    Text Solution

    |

  10. Find the inverse the matrix (if it exists)given in[1-1 2 0 2-3 3-2 4]

    Text Solution

    |

  11. Find the inverse the matrix (if it exists)given in[0 0 0 0cosalphasina...

    Text Solution

    |

  12. If A=|[3, 2], [7, 5]| and B=|[6 ,7], [8, 9]| , verify that (A B)^(-1)=...

    Text Solution

    |

  13. If A=[[3,1],[-1,2]], I=[[1,0],[0,1]] and O=[[0,0],[0,0]], show that A...

    Text Solution

    |

  14. Solve system of linear equations, using matrix method, x- y" "+" "2...

    Text Solution

    |

  15. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

    Text Solution

    |

  16. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

    Text Solution

    |

  17. Let A be a non-singular square matrix of order 3 xx3. Then |adj A| is ...

    Text Solution

    |

  18. If A is an invertible matrix, then det(A^(-1)) is equal to det(A) (...

    Text Solution

    |